Help my phone stopped working!!!

I had it charging all day and was barely using it. (I am at work so I can't use it much). I get home to check my messages for lunch and it was turned off. I try turning it back on, it goes to the Samsung Galaxy s4 page and then shuts off. I figure the battery is dead so I plug it in to FOUR DIFFERENT CHARGERS. Nothing happened. No red light. Nothing. Tested the cords with my Galaxy Tab 3 and the cords work fine. So I get my spare battery which was fully charged and put that battery in it. It turns on, gets to the home screen (FINALLY). Said it had a full battery and then the phone is off again!!

This phone has NO water damage, or broken anything of any kind. I don't know what to do.

Yes.
Phone isn't under warranty as it has been over a year. I can send it in and if they decide that I did damage to it myself (even though I know I didn't) they can charge me whatever they feel is necessary to fix it. Looks like I will just have to trash it.